Search:

More info on Kilogram

Kilogram: Map

Advertisements

Wikipedia article:

Map showing all locations mentioned on Wikipedia article:

The kilogram (symbol: kg) is the base unit of mass in the
International System of
Units (SI, from the French ). The kilogram is defined as being
equal to the mass of the International Prototype Kilogram
(IPK), which is almost exactly equal to the mass
of one liter of water. It is the only SI base
unit with an SI prefix as part of its
name. It is also the only SI unit that is still defined by an
artifact rather than a fundamental
physical property that can be reproduced in different
laboratories.

In everyday usage, the mass of an object, which is measured in
kilograms, is often referred to as its weight. However, the term weight in strict
scientific contexts refers to the gravitationalforce of an
object. Throughout most of the world, force is measured with the SI
unit newton and the non-SI unit
kilogram-force. Similarly, the
avoirdupois (or
international)pound, used in both the Imperial system and U.S. customary units, is a
unit of mass and its related unit of force is the pound-force. The avoirdupois pound is defined as
exactly ,

making one kilogram approximately equal to 2.2046 avoirdupois
pounds.

Many units in the SI system are defined relative to the kilogram so
its stability is important. After the International Prototype
Kilogram had been found to vary in mass over time, the International
Committee for Weights and Measures (known also by its
French-language initials CIPM) recommended in 2005 that the
kilogram be redefined in terms of a fundamental constant of nature.
No final decision is expected before 2011.

Nature of mass

The kilogram is a unit of mass, the measurement
of which corresponds to the general, everyday notion of how “heavy”
something is. However, mass is actually an inertial property; that is, the tendency of an
object to remain at constant velocity unless acted upon by an
outside force. According to Sir Isaac Newton's -year-old laws of motion and an important
formula that sprang from his work, an object with a mass,
m, of one kilogram will accelerate, a, at one meter per second per second (about
one-tenth the acceleration due to earth’s gravity)In professional metrology (the science of measurement), the
acceleration of earth’s gravity is taken as standard gravity (symbol:
gn),
which is defined as precisely meters per square second
(m/s2). The expression means that for every second
that elapses, velocity changes an additional 1 meter per
second. In more familiar terms: an acceleration of 1
m/s2 can also be expressed as a rate of change in
velocity of precisely 3.6 km/h per second (≈2.2 mph per
second). when acted upon by a force, F, of one newton.

While the weight of matter is
entirely dependent upon the strength of gravity, the mass
of matter is invariant.Matter has invariant mass assuming it is not
traveling at a relativistic speed with respect
to an observer. According to Einstein’s theory of special relativity, the relativistic mass (apparent mass
with respect to an observer) of an object or particle with rest
mass m0 increases with its speed as M
= γm0 (where γ is the Lorentz factor). This effect is vanishingly
small at everyday speeds, which are many orders of magnitude less than the
speed of light. For example, to
change the mass of a kilogram by 1 μg (1 ppb, about the level of detection by current technology)
would require moving at 0.045% of the speed of light, or 134 km/s
(300000 mph).

As regards the kilogram, relativity’s effect upon the constancy
of matter’s mass is simply an interesting scientific phenomenon
that has zero effect on the definition of the kilogram and its
practical realizations. Accordingly, for astronauts in microgravity, no effort is required to
hold objects off the cabin floor; they are “weightless.” However,
since objects in microgravity still retain their mass and inertia,
an astronaut must exert ten times as much force to accelerate a 10
kilogram object at the same rate as a 1 kilogram object.

On earth, a common swing set can demonstrate the relationship of
force, mass, and acceleration without being appreciably influenced
by weight (downward force). If one were to stand behind a large
adult sitting stationary in a swing and give him a strong push, the
adult would accelerate relatively slowly and swing only a limited
distance forwards before beginning to swing backwards. Exerting
that same effort while pushing on a small child would produce much
greater acceleration.

History

Early definitions

On 7 April 1795, the gram was decreed in France
to be equal to “the absolute weight of a volume of water equal to
the cube of the hundredth part of the meter, at the temperature of
melting ice.”Since trade and commerce typically involve items
significantly more massive than one gram, and since a mass standard
made of water would be inconvenient and unstable, the regulation of
commerce necessitated the manufacture of a practical realization of the water-based
definition of mass. Accordingly, a
provisional mass standard was made as a single-piece, metallic
artifact one thousand times more massive
than the gram—the kilogram.

At the same time, work was commissioned to precisely determine the
mass of a cubic decimeter (one liter) of
water. Although the decreed definition of the kilogram specified
water at 0 °C—its highly stable temperature point—the
French chemist, Louis
Lefèvre-Gineau and the Italian naturalist, Giovanni Fabbroni after several years of
research chose to redefine the standard in 1799 to water’s most
stable density point: the temperature at which water
reaches maximum density, which was measured at the time as 4
°C.They concluded that one cubic decimeter of water at its maximum
density was equal to 99.9265% of the target mass of the provisional
kilogram standard made four years earlier.The provisional kilogram
standard had been fabricated in accordance with a single,
inaccurate measurement of the density of water made earlier by
Antoine Lavoisier and René Just Haüy, which showed that
one cubic decimeter of distilled water at 0 °C had a mass of 18,841
grains in France’s soon-to-be-obsoleted poids de marc system. The
newer, highly accurate measurements by Lefèvre Gineau and Fabbroni
concluded that the mass of a cubic decimeter of water at the new
temperature of 4 °C—a condition at which water is denser—was
actually less massive, at 18,827.15 grains, than the
earlier inaccurate value assumed for 0 °C water.

France’s metric system had been championed by Charles Maurice de
Talleyrand Périgord. On 30 March 1791, four days after
Talleyrand forwarded a specific proposal on how to proceed with the
project, the French government ordered a committee known as the
Academy to commence work on accurately determining the magnitude of
the base units of the new metric system. The Academy divided the
task among five commissions. The commission charged with
determining the mass of a cubic decimeter of water originally
comprised Lavoisier and Haüy but their work was finished by Louis
Lefèvre Gineau and Giovanni Fabbroni.

Neither Lavoisier nor Haüy can be blamed for participating in an
initial—and inaccurate—measurement and for leaving the final work
to Lefèvre‑Gineau and Fabbroni to finish in 1799. As a member of
the Ferme
générale, Lavoisier was also one of France’s 28 tax
collectors. He was consequently convicted of treason during the
waning days of the Reign of Terror
period of the French Revolution
and beheaded on 8 May 1794. Lavoisier’s partner, Haüy, was also
thrown into prison and was himself at risk of going to the
guillotine but his life was spared after a renown French naturalist
interceded.

That same year, 1799, an all-platinum kilogram prototype was fabricated with the objective that
it would equal, as close as was scientifically feasible for the
day, the mass of one cubic decimeter of water at 4 °C.

The prototype was presented to the Archives of the Republic in
June and on 10 December 1799, the prototype was formally ratified
as the Kilogramme des Archives (Kilogram of the Archives)
and the kilogram was defined as being equal to its mass.

This standard stood for the next ninety years.

International Prototype Kilogram

Since 1889, the SI
system defines the magnitude of the
kilogram to be equal to the mass of the International Prototype
Kilogram, often referred to in the professional metrology world as the “IPK”. The IPK is made of a
platinum alloy known as “Pt 10Ir”, which is
90% platinum and 10% iridium (by mass) and is machined into a
right-circular cylinder (height = diameter) of 39.17 millimeters to minimize its surface area.New
Techniques in the Manufacture of Platinum-Iridium Mass
Standards, T. J. Quinn, Platinum Metals Rev., 1986,
30, (2), pp. The addition of 10% iridium improved
upon the all-platinum Kilogram of the Archives by greatly
increasing hardness while still retaining
platinum’s many virtues: extreme resistance to oxidation, extremely high density, satisfactory electrical and thermal conductivities, and low
magnetic susceptibility. The
IPK and its six sister copies are stored
at the International
Bureau of Weights and Measures (known by its French-language
initials BIPM) in an environmentally monitored safe in the lower
vault located in the basement of the BIPM’s House of Breteuil in
Sèvres on the outskirts of Paris (see
External images, below for
photographs). Three independently controlled keys are required to
open the vault. Official copies of the IPK were made available to
other nations to serve as their national standards. These are
compared to the IPK roughly every 50 years.

The IPK is one of three cylinders made in 1879. In 1883, it was
found to be indistinguishable from the mass of the Kilogram of the
Archives made eighty-four years prior, and was formally ratified as
the kilogram by the 1st CGPM in 1889.
Modern measurements of the density of Vienna Standard Mean Ocean
Water—purified water that has a carefully controlled isotopic
composition—show that a cubic decimeter of water at its point of
maximum density, 3.984 °C, has a mass that is 25.05 parts per million less than the
kilogram.Water Structure and Science, Water Properties, Density
maximum (and molar volume) at temperature of maximum density,
a (by London South Bank University). Link to Web
site. This small difference, and the fact that the mass of the
IPK was indistinguishable from the mass of the Kilogram of the
Archives, speak volumes of the scientists’ skills over years ago
when making their measurements of water’s properties and in
manufacturing the Kilogram of the Archives.

Stability of the International Prototype Kilogram

By definition, the error in the measured value of the IPK’s mass is exactly zero; the IPK is
the kilogram. However, any changes in the IPK’s mass over time can
be deduced by comparing its mass to that of its official copies
stored throughout the world, a process called “periodic
verification.” For instance, the U.S. owns four 10% iridium (Pt
10Ir) kilogram standards, two of which, K4 and K20, are from the
original batch of 40 replicas delivered in
1884. The K20 prototype was designated as the primary national standard of mass for the U.S.
Both of these, as well as those from other nations, are
periodically returned to the BIPM for verification.Extraordinary
care is exercised when transporting prototypes. In 1984, the K4 and
K20 prototypes were hand-carried in the passenger section of
separate commercial airliners.

Note that none of the replicas has a mass precisely equal to that
of the IPK; their masses are calibrated and documented as offset
values. For instance, K20, the U.S.’s primary standard, originally
had an official mass of micrograms (µg) in 1889; that is to say,
K20 was 39 µg less than the IPK. A verification performed in 1948
showed a mass of The latest verification performed in 1999 shows a
mass precisely identical to its original 1889 value. Quite unlike
transient variations such as this, the U.S.’s check standard, K4, has persistently declined in
mass relative to the IPK—and for an identifiable reason. Check
standards are used much more often than primary standards and are
prone to scratches and other wear. K4 was originally delivered with
an official mass of in 1889, but as of 1989 was officially
calibrated at and ten years later was Over a period of 110 years,
K4 lost 41 µg relative to the IPK.

Beyond the simple wear that check standards can experience, the
mass of even the carefully stored national prototypes can drift
relative to the IPK for a variety of reasons, some known and some
unknown. Since the IPK and its replicas are stored in air (albeit
under two or more nested bell jars), they
gain mass through adsorption of
atmospheric contamination onto their surfaces. Accordingly, they
are cleaned in a process the BIPM developed between 1939 and 1946
known as “the BIPM cleaning method” that comprises firmly rubbing
with a chamois soaked in equal parts
ether and ethanol,
followed by steam cleaning with
bi-distilled water, and allowing the
prototypes to settle for days before
verification.Before the BIPM’s published report in 1994 detailing
the relative change in mass of the prototypes, different standard
bodies used different techniques to clean their prototypes. The
NIST’s practice before then was to soak and rinse its two
prototypes first in benzene, then in
ethanol, and to then clean them with a jet of bi-distilled water
steam. Cleaning the prototypes removes between 5 and 60 µg of
contamination depending largely on the time elapsed since the last
cleaning. Further, a second cleaning can remove up to 10 µg more.
After cleaning—even when they are stored under their bell jars—the
IPK and its replicas immediately begin gaining mass again. The BIPM
even developed a model of this gain and concluded that it averaged
1.11 µg per month for the first 3 months after cleaning and then
decreased to an average of about 1 µg per year thereafter. Since
check standards like K4 are not cleaned for routine calibrations of
other mass standards—a precaution to minimize the potential for
wear and handling damage—the BIPM’s model has been used as an
“after cleaning” correction factor.

K48, above, came from the second batch
of kilogram replicas to be produced.

It was delivered to Denmark in 1949 with an official mass of
Like all other replicas, it is stored under two nested bell jars
virtually all the time.

Still, its mass and that of the IPK diverged markedly in only
40 years; the mass of K48 was certified as during the periodic
verification.

the first forty official copies are made of the same alloy as the
IPK and are stored under similar conditions, periodic verifications
using a large number of replicas—especially the national primary
standards, which are rarely used—can convincingly demonstrate the
stability of the IPK. What has become clear after the third
periodic verification performed between 1988 and 1992 is that
masses of the entire worldwide ensemble of prototypes have been
slowly but inexorably diverging from each other. It is also clear
that the official copies have all gained mass, some more than 50
µg, over the last century, in comparison to the IPK. The reason for
this drift has eluded physicists who have dedicated their careers
to the SI unit of mass. No plausible mechanism has been proposed to
explain either a steady decrease in the mass of the IPK, or an
increase in that of its replicas dispersed throughout the
world.Note that if the between the IPK and its replicas was
entirely due to wear, the IPK would have to have lost 150 million
billion more platinum and iridium atoms over the last century than
its replicas. That there would be this much wear, much less a
difference of this magnitude, is thought unlikely; 50 µg
is roughly the mass of a fingerprint. Specialists at the BIPM in
1946 carefully conducted cleaning experiments and concluded that
even vigorous rubbing with a chamois—if done carefully—did
not alter the prototypes’ mass. More recent cleaning experiments at
the BIPM, which were conducted on one particular prototype (K63),
and which benefited from the then-new NBS 2 balance, demonstrated 2
µg stability.

Many theories have been advanced to explain the divergence in
the masses of the prototypes. One theory posits that the relative
change in mass between the IPK and its replicas is not one of loss
at all and is instead a simple matter that the IPK has gained
less than the replicas. This theory begins with the
observation that the IPK is uniquely stored under three nested bell
jars whereas its six sister copies stored alongside it in the vault
as well as the other replicas dispersed throughout the world are
stored under only two. This theory is also founded on two other
facts: that platinum has a strong affinity for mercury, and that
atmospheric mercury is significantly more abundant in the
atmosphere today than at the time the IPK and its replicas were
manufactured. The burning of coal is a major contributor to
atmospheric mercury and both Denmark and Germany have high coal
shares in electrical generation. Conversely, electrical generation
in France, where the IPK is stored, is mostly nuclear. This theory
is supported by the fact that the mass divergence rate—relative to
the IPK—of Denmark’s prototype, K48, since it took possession in
1949 is an especially high 78 µg per century while that of
Germany’s prototype has been even greater at ever since it took
possession of K55 in 1954. However, still other data for other
replicas isn’t supportive of this theory. This mercury absorption
theory is just one of many advanced by the specialists to account
for the relative change in mass. To date, each theory has either
proven implausible, or there are insufficient data or technical
means to either prove or disprove it.Conjecture why the IPK
drifts, R. Steiner, NIST, 11 Sept. 2007. This
relative nature of the changes amongst the world’s
kilogram prototypes is often misreported in the popular press, and
even some notable scientific magazines, which often state that the
IPK simply “lost 50 µg” and omit the very important caveat of
“in comparison to its official copies.”Even well respected organizations incorrectly
represent the relative nature of the mass divergence as being one
of mass loss, as exemplified by this site at Science Daily, and this
site at PhysOrg.com, and this
site at Sandia National Laboratories. The root of the problem
is often the reporters’ failure to correctly interpret or
paraphrase nuanced scientific concepts, as exemplified by this 12
September 2007 story by the Associated Press published on PhysOrg.com. In that AP story, Richard Davis—who
used to be the NIST’s kilogram specialist and now works for the
BIPM in France—was correctly quoted by the AP when he stated that
the mass change is a relative issue. Then the AP summarized the
nature of issue with this lead-in to the story: “A kilogram
just isn't what it used to be. The 118-year-old cylinder that is
the international prototype for the metric mass, kept tightly under
lock and key outside Paris, is mysteriously losing weight — if
ever so slightly.” Like many of the above-linked sites, the AP
also misreported the age of the IPK, using the date of its adoption
as the mass prototype, not the date of the cylinder’s manufacture.
This is a mistake even Scientific
American fell victim to in a print edition. Moreover,
there are no technical means available to determine whether or not
the entire worldwide ensemble of prototypes suffers from even
greater long-term trends upwards or downwards because their mass
“relative to an invariant of nature is unknown at a level below
1000 µg over a period of 100 or even 50 years.” Given the lack of
data identifying which of the world’s kilogram prototypes has been
most stable in absolute terms, it is equally as valid to state that
the first batch of replicas has, as a group, gained an average of
about 25 µg over one hundred years in comparison to the IPK.The
mean change in mass of the first batch of replicas relative to the
IPK over one hundred years is +23.5 µg with a standard deviation of
30 µg. Per The Third Periodic Verification of National
Prototypes of the Kilogram G. Girard, Metrologia '31
(1994) Pg. 323, Table 3. Data is for prototypes K1, K5, K6,
K7, K8(41), K12, K16, K18, K20, K21, K24, K32, K34, K35, K36, K37,
K38, and K40; and excludes K2, K23, and K39, which are treated as
outliers. This is a larger data set than is shown in the chart at
the top of this section, which corresponds to Figure 7 of G.
Girard’s paper.

What is known specifically about the IPK is that it
exhibits a short-term instability of about 30 µg over a period of
about a month in its after-cleaned mass.Report to the CGPM, 14th
meeting of the Consultative Committee for Units (CCU), April 2001,
2. (ii); General Conference on Weights and Measures, 22nd
Meeting, October 2003, which stated “The kilogram is in need
of a new definition because the mass of the prototype is known to
vary by several parts in 108 over periods of time of the
order of a month…” ( 3.2
MB ZIP file, here). The precise reason for this short-term
instability is not understood but is thought to entail surface
effects: microscopic differences between the prototypes’ polished
surfaces, possibly aggravated by hydrogen
absorption due to catalysis of the
volatile organic compounds
that slowly deposit onto the prototypes as well as the hydrocarbon-based solvents used to clean
them.BBC, Getting the measure of a kilogram.

Scientists are seeing far greater variability in the prototypes
than previously believed. The increasing divergence in the masses
of the world’s prototypes and the short-term instability in the IPK
has prompted research into improved methods to obtain a smooth
surface finish using diamond-turning on newly manufactured replicas
and has intensified the search for a new definition of the
kilogram. See Proposed
future definitions, below.General section citations:
Recalibration of the U.S. National Prototype Kilogram, R.
S. Davis, Journal of Research of the National Bureau of Standards,
90, No. 4, 1985 ( 5.5 MB PDF, here); and The Kilogram and
Measurements of Mass and Force, Z. J. Jabbour et al.,
J. Res. Natl. Inst. Stand. Technol. 106, 2001, (
3.5 MB PDF, here)

Importance of the kilogram

The magnitude of many of the units
comprising the SI system of measurement, including most of those
used in the measurement of electricity and light, are highly
dependent upon the stability of a -year-old, golf ball-size
cylinder of metal stored in a vault in France.

The stability of the IPK is crucial
because the kilogram underpins much of the SI system of measurement
as it is currently defined and structured. For instance, the
newton is defined as the force
necessary to accelerate one kilogram at one meter per second squared. If the
mass of the IPK were to change slightly, so too must the newton by
a proportional degree. In turn, the pascal, the SI unit of pressure, is defined in terms of the newton. This
chain of dependency follows to many other SI units of measure. For
instance, the joule, the SI unit of energy, is defined as that expended when a force of
one newton acts through one meter. Next to be
affected is the SI unit of power,
the watt, which is one joule per second. The
ampere too is defined relative to the newton,
and ultimately, the kilogram. With the magnitude of the primary units of electricity thus
determined by the kilogram, so too follow many others; namely, the
coulomb, volt, tesla, and weber.
Even units used in the measure of light would be affected; the
candela—following the change in the would in
turn affect the lumen and lux.

Because the magnitude of many of the units comprising the SI system
of measurement is ultimately defined by the mass of a -year-old,
golf ball-sized piece of metal, the quality of the IPK must be
diligently protected to preserve the integrity of the SI system.
Yet, in spite of the best stewardship, the average mass of the
worldwide ensemble of prototypes and the mass of the IPK have
likely diverged another µg since the third periodic verification
years ago.Assuming the past trend continues, whereby the mean
change in mass of the first batch of replicas relative to the IPK
over one hundred years was +23.5 σ30 µg. Further, the world’s national
metrology laboratories must wait for the fourth periodic
verification to confirm whether the historical trends
persisted.

Fortunately, definitions of the
SI units are quite different from their practical realizations. For instance, the
meter is defined as the distance
light travels in a vacuum during a time interval of of a second.
However, the meter’s practical realization typically takes
the form of a helium-neon laser, and the meter’s length is
delineated—not defined—as
wavelengths of light from this laser. Now suppose that the official
measurement of the second was found to have drifted by a few
parts per billion (it is actually
exquisitely stable). There would be no automatic effect on the
meter because the second—and thus the meter’s length—is abstracted via the laser comprising the meter’s
practical realization. Scientists performing meter calibrations
would simply continue to measure out the same number of laser
wavelengths until an agreement was reached to do otherwise. The
same is true with regard to the real-world dependency on the
kilogram: if the mass of the IPK was found to have changed
slightly, there would be no automatic effect upon the other units
of measure because their practical realizations provide an
insulating layer of abstraction. Any discrepancy would eventually
have to be reconciled though because the virtue of the SI system is
its precise mathematical and logical harmony amongst its units. If
the IPK’s value were definitively proven to have changed, one
solution would be to simply redefine the kilogram as being equal to
the mass of the IPK plus an offset value, similarly to what is
currently done with its replicas; e.g., “the kilogram is equal to
the mass of the (equivalent to 42 µg).

The long-term solution to this problem, however, is to liberate the
SI system’s dependency on the IPK by developing a practical
realization of the kilogram that can be reproduced in different
laboratories by following a written specification. The units of
measure in such a practical realization would have their magnitudes
precisely defined and expressed in terms of fundamental physical
constants. While major portions of the SI system would still be
based on the kilogram, the kilogram would in turn be based on
invariant, universal constants of nature. While this is a
worthwhile objective and much work towards that end is ongoing, no
alternative has yet achieved the uncertainty of a couple parts in
108 (~20 µg) required to improve upon the IPK. However,
, the U.S.’s National
Institute of Standards and Technology (NIST) had an
implementation of the watt balance that
was approaching this goal, with a demonstrated uncertainty of 36
µg.Uncertainty Improvements of the NIST Electronic
Kilogram, RL Steiner et al., Instrumentation and
Measurement, IEEE Transactions on, 56 Issue 2,
April 2007, See Watt balance,
below.

Proposed future definitions

In the following section, wherever numeric equalities are
shown in ‘concise form’—such as —the two digits between the
parentheses denotes the uncertainty at
1σ standard deviation (68%
confidence level) in the two least significant digits of the
significand.

The kilogram is the only SI unit that is still defined by an
artifact. Note that the meter was also once
defined as an artifact (a single platinum-iridium bar with two
marks on it). However, it was eventually redefined in terms of
invariant, fundamental constants of nature (the wavelength of light
emitted by krypton, which depends on the
speed of light and Planck's constant) so that the standard
can be reproduced in different laboratories by following a written
specification. Today, physicists are investigating various
approaches to do the same with the kilogram. Some of the approaches
are fundamentally very different from each other. Some are based on
equipment and procedures that enable the reproducible production of
new, kilogram-mass prototypes on demand (albeit with extraordinary
effort) using measurement techniques and material properties that
are ultimately based on, or traceable to, fundamental constants.
Others are devices that measure either the acceleration or weight
of hand-tuned, kilogram test masses and which express their
magnitudes in electrical terms via special
components that permit traceability to fundamental constants.
Measuring the weight of test masses requires the precise
measurement of the strength of gravity in laboratories. All
approaches would precisely fix one or more constants of nature at a
defined value. These different approaches are as follows:

Atom-counting approaches

Carbon-12

Though not offering a practical realization, this definition would
precisely define the magnitude of the kilogram in terms of a
certain number of carbon 12 atoms. Carbon
12 (12C) is an isotope of carbon.
The mole is currently defined as “the
quantity of entities (elementary particles like atoms or molecules)
equal to the number of atoms in 12 grams of carbon 12.” Thus, the
current definition of the mole requires that (83⅓) moles of
12C has a mass of precisely one kilogram. The number of
atoms in a mole, a quantity known as the Avogadro constant, is experimentally
determined, and the current best estimate of its value is entities
per mole (CODATA, 2006).
This new definition of the kilogram proposes to fix the Avogadro
constant at precisely with the kilogram being defined as “the mass
equal to that of atoms of 12C.”

The accuracy of the measured value of the Avogadro constant is
currently limited by the uncertainty in the value of the Planck constant—a measure relating the
energy of photons to their frequency. That relative standard
uncertainty has been 50 parts per billion (ppb) since 2006. By
fixing the Avogadro constant, the practical effect of this proposal
would be that the uncertainty in the mass of a 12C
atom—and the magnitude of the kilogram—could be no better than the
current 50 ppb uncertainty in the Planck constant. Under this
proposal, the magnitude of the kilogram would be subject to future
refinement as improved measurements of the value of the Planck
constant become available; electronic realizations of the kilogram
would be recalibrated as required. Conversely, an electronic
definition of the kilogram (see Electronic approaches, below),
which would precisely fix the Planck constant, would continue to
allow 83⅓ moles of 12C to have a mass of precisely one
kilogram but the number of atoms comprising a mole (the Avogadro
constant) would continue to be subject to future refinement.

A variation on a 12C-based definition proposes to define
the Avogadro constant as being precisely 84,446,8863 (≈
) atoms. An imaginary realization of a 12-gram mass prototype would
be a cube of 12C atoms measuring precisely 84,446,886
atoms across on a side. With this proposal, the kilogram would be
defined as “the mass equal to 84,446,8863 × 83⅓ atoms of
12C.” The value 84,446,886 was chosen because it has a
special property; its cube (the proposed new value for the Avogadro
constant) is evenly divisible by twelve. Thus with this definition
of the kilogram, there would be an integer number of atoms in one
gram of 12C: 50,184,508,190,229,061,679,538 atoms.The
uncertainty in the Avogadro constant narrowed since this proposal
was first submitted to American
Scientist for publication. The 2006 CODATA value for the
Avogadro constant has a relative standard uncertainty of 50 parts
per billion and the only cube root values within this uncertainty
must fall within the range of 84,446,889.8 ±1.4; that is, there are
only three integer cube roots (…89, …90, and …91) in this range and
the value 84,446,886 falls outside of it. Unfortunately, none of
the three integer values within the range possess the property of
their cubes being divisible by twelve; one gram of 12C
could not comprise an integer number of atoms. If the value
84,446,886 was adopted to define the kilogram, many other constants
of nature and electrical units would have to be revised an average
of about 0.13 part per million. The straightforward adjustment to
this approach advanced by the group would instead define the
kilogram as “the mass equal to 84,446,8903 × 83⅓ atoms
of carbon 12.” This proposed value for the Avogadro constant (≈ )
falls neatly within the 2006 CODATA value of ) and the proposed
definition of the kilogram produces an integer number of atoms in
12 grams of carbon 12 (602,214,183,858,071,454,769,000 atoms), but
not for 1 gram or 1 kilogram.

Avogadro project

Another Avogadro constant-based approach, known as the Avogadro
project, would define and delineate the kilogram as a
softball-size (93.6 mm diameter) sphere of silicon atoms. Silicon was chosen because a
commercial infrastructure with mature processes for creating
defect-free, ultra-pure monocrystalline silicon already exists to
service the semiconductor industry. To
make a practical realization of the kilogram, a silicon boule (a rod-like, single-crystal ingot)
would be produced. Its isotopic composition
would be measured with a mass
spectrometer to determine its average relative atomic mass. The
boule would be cut, ground, and polished into spheres. The size of
a select sphere would be measured using optical interferometry to an uncertainty of about 0.3
nm on the radius—roughly a single atomic layer. The precise lattice
spacing between the atoms in its crystal structure (≈192 pm) would
be measured using a scanning X-ray interferometer. This permits its
atomic spacing to be determined with an uncertainty of only three
parts per billion. With the size of the sphere, its average atomic
mass, and its atomic spacing known, the required sphere diameter
can be calculated with sufficient precision and uncertainty to
enable it to be finish-polished to a target mass of one
kilogram.

Experiments are being performed on the Avogadro Project’s silicon
spheres to determine whether their masses are most stable when
stored in a vacuum, a partial vacuum, or ambient pressure. However,
no technical means currently exist to prove a long-term stability
any better than that of the IPK’s because the most sensitive and
accurate measurements of mass are made with dual-panbalances like the BIPM’s FB 2
flexure-strip balance (see External
links, below). Balances can only compare the mass of a
silicon sphere to that of a reference mass. Given the latest
understanding of the lack of long-term mass stability with the IPK
and its replicas, there is no known, perfectly stable mass artifact
to compare against. Single-panscale capable of measuring weight
relative to an invariant of nature with a long-term uncertainty of
only parts per billion do not yet exist. Another issue to be
overcome is that silicon oxidizes and forms a thin layer
(equivalent to silicon atoms) of silicon
dioxide (quartz) and silicon monoxide. This layer slightly
increases the mass of the sphere, an effect which must be accounted
for when polishing the sphere to its finish dimension. Oxidation is
not an issue with platinum and iridium, both of which are noble metals that are roughly as cathodic as oxygen and therefore don’t
oxidize unless coaxed to do so in the laboratory. The presence of
the thin oxide layer on a silicon-sphere mass prototype places
additional restrictions on the procedures that might be suitable to
clean it to avoid changing the layer’s thickness or oxide stoichiometry.

All silicon-based approaches would fix the Avogadro constant but
vary in the details of the definition of the kilogram. One approach
would use silicon with all three of its natural isotopes present.
About 7.78% of silicon comprises the two heavier isotopes:
29Si and 30Si. As described in Carbon 12 above, this method would
define the magnitude of the kilogram in terms of a certain
number of 12C atoms by fixing the Avogadro constant; the
silicon sphere would be the practical realization. This
approach could accurately delineate the magnitude of the kilogram
because the masses of the three silicon nuclides relative to 12C are known with
great precision (relative uncertainties of 1 ppb or better). An alternative method for
creating a silicon sphere-based kilogram proposes to use isotopic separation techniques to enrich
the silicon until it is nearly pure 28Si, which has a
relative atomic mass of . With this approach, the Avogadro constant
would not only be fixed, but so too would the atomic mass of
28Si. As such, the definition of the kilogram would be
decoupled from 12C and the kilogram would instead be
defined as · atoms of 28Si (≈ fixed
moles of 28Si atoms). Physicists could elect to define
the kilogram in terms of 28Si even when kilogram
prototypes are made of natural silicon (all three isotopes
present). Even with a kilogram definition based on 28Si,
a silicon-sphere prototype made of nearly pure 28Si
would necessarily deviate slightly from the defined number of moles
of silicon to compensate for various chemical and isotopic
impurities as well as the effect of surface oxides.

Ion accumulation

Another Avogadro-based approach, ion
accumulation, since abandoned, would have defined and delineated
the kilogram by precisely creating new metal prototypes on demand.
It would have done so by accumulating gold or
bismuthions (atoms
stripped of an electron) and counted them by measuring the
electrical current required to neutralize the ions. Gold
(197Au) and bismuth (209Bi) were chosen
because they can be safely handled and have the two highest
atomic masses among the mononuclidic elements that can be
treated as if it is virtually non-radioactive (bismuth) or is
perfectly stable (gold). See also Table of nuclides.In 2003,
the same year the first gold-deposition experiments were conducted,
physicists found that the only naturally occurring isotope of
bismuth, 209Bi, is actually very slightly radioactive, with the longest known
radioactive half-life of any naturally
occurring element that decays via alpha
radiation—a half-life of . As this is 1.4 billion times the age
of the universe, 209Bi is considered a stable isotope
for most practical applications (those unrelated to such
disciplines as nucleocosmochronology and geochronology). In other terms, of the bismuth
that existed on earth 4.567 billion years ago still exists today.
Only two mononuclidic elements are heavier than bismuth and only
one approaches its stability: thorium. Long
considered a possible replacement for uranium in nuclear reactors,
thorium can cause cancer when inhaled because it is over 1.2
billion times more radioactive than bismuth. It also has such a
strong tendency to oxidize that its powders are pyrophoric. These characteristics make thorium
unsuitable in ion-deposition experiments. See also Isotopes of bismuth, Isotopes of gold and Isotopes of thorium.

With a gold-based definition of the kilogram for instance, the
relative atomic mass of gold could have been fixed as precisely ,
from the current value of . As with a definition based upon carbon
12, the Avogadro constant would also have been fixed. The kilogram
would then have been defined as “the mass equal to that of
precisely · atoms of gold” (precisely
3,057,443,620,887,933,963,384,315 atoms of gold or about fixed
moles).

In 2003, German experiments with gold at a current of only 10 µA
demonstrated a relative uncertainty of 1.5%. Follow-on experiments
using bismuth ions and a current of 30 mA were expected to
accumulate a mass of 30 g in six days and to have a relative
uncertainty of better than 1 part in 106. Ultimately,
ion accumulation approaches proved to be unsuitable. Measurements
required months and the data proved too erratic for the technique
to be considered a viable future replacement to the IPK.

Among the many technical challenges of the ion-deposition apparatus
was obtaining a sufficiently high ion current (mass deposition
rate) while simultaneously decelerating the ions so they could all
deposit onto a target electrode embedded in a balance pan.
Experiments with gold showed the ions had to be decelerated to very
low energies to avoid sputtering
effects—an phenomenon whereby ions that had already been counted
ricochet off the target electrode or even dislodged atoms that had
already been deposited. The deposited mass fraction in the 2003
German experiments only approached very close to 100% at ion
energies of less than around 1 eV
(<1 km=""></1>s for gold).

If the kilogram had been defined as a precise quantity of gold or
bismuth atoms deposited with an electric current, not only would
the Avogadro constant and the atomic mass of gold or bismuth had to
have been precisely fixed, but also the value of the elementary charge (e), likely to (from the present 2006
CODATA value of ). Doing so would have effectively defined the
ampere as a flow of
(6,241,509,647,120,417,390) electrons per second past a fixed point
in an electric circuit. The SI unit of mass would have been fully
defined by having precisely fixed the values of the Avogadro
constant and elementary charge, and by exploiting the fact that the
atomic masses of bismuth and gold atoms are invariant, universal
constants of nature.

Beyond the slow speed of making a new mass standard and the poor
reproducibility, there were other intrinsic shortcomings to the ion
accumulation approach that proved to be formidable obstacles to
ion-accumulation-based techniques becoming a practical realization.
The apparatus necessarily required that the deposition chamber have
an integral balance system to enable the convenient calibration of
a reasonable quantity of transfer
standards relative to any single internal ion-deposited
prototype. Furthermore, the mass prototypes produced by ion
deposition techniques would have been nothing like the freestanding
platinum-iridium prototypes currently in use; they would have been
deposited onto—and become part of—an electrode imbedded into one
pan of a special balance integrated into the device. Moreover, the
ion-deposited mass wouldn’t have had a hard, highly polished
surface that can be vigorously cleaned like those of current
prototypes. Gold, while dense and a noble
metal (resistant to oxidation and the formation of other
compounds), is extremely soft so an internal gold prototype would
have to be kept well isolated and scrupulously clean to avoid
contamination and the potential of wear from having to remove the
contamination. Bismuth, which is an inexpensive metal used in
low-temperature solders, slowly oxidizes when exposed to
room-temperature air and forms other chemical compounds and so
would not have produced stable reference masses unless it was
continually maintained in a vacuum or inert atmosphere.

The watt balance requires exquisitely precise measurement of
gravity in a laboratory (see “FG‑5 absolute gravimeter” in
External images, below).
For instance, the NIST compensates for earth’s gravity gradient of
3.09 µGal per centimeter when the
elevation of the center of the gravimeter
differs from that of the nearby test mass in the watt balance; a
change in the weight of a one-kilogram test mass that equates to
about 3.16 µg/cm.

In April 2007, the NIST’s
implementation of the watt balance demonstrated a combined relative
standard uncertainty (CRSU) of 36 µg and a short-term resolution of
µg. The
UK’s National Physical Laboratory’s watt balance demonstrated a CRSU of 70.3 µg in
2007."An initial measurement of Planck's constant using the NPL
Mark II watt balance", I.A. Robinson et al.,
Metrologia44 (2007),
NPL: NPL Watt BalanceThat watt balance was
disassembled and shipped in 2009 to Canada’s Institute for National
Measurement Standards (part of the National
Research Council), where research and development with the device
could continue.

With the watt balance, the kilogram would be redefined and
internationally recognized in terms of two invariants of nature:
the speed of light (c) and
the Planck constant (h),
which is a measure that relates the energy of photons to their frequency. The Planck constant would
be fixed; for example, to (from the 2006 CODATA value of ). The
kilogram would relate to these two fundamental constants of nature
via the formula , which is to say, the kilogram would be equal to
the square of the speed of light divided by the Planck constant
where the defined amount of energy ultimately takes the form of a
simple frequency. The kilogram would thus be defined as “the mass
of a body at rest whose equivalent energy equals the energy of
photons whose frequencies sum to

The SI unit, hertz (the reciprocal second) cannot normally be used as a measure of energy. When referring to a watt balance-based definition of the kilogram, the disciplines of professional metrology and physics customarily refer to the quotient of E/h (energy divided by a factor relating the energy of photons to their frequency) as a frequency, f, and add a crucial caveat in prose explaining that the unit of measure, hertz, represents an energy equivalent to that of photons whose frequencies sum to the stated value. However, even authoritative sources will, when communicating to a general-interest audience, sometimes state that one kilogram is equivalent to and attach no explanation (other than displaying the formula c2/h) that the true measure is a corresponding energy, as exemplified here at the NIST’s Fundamental physical constants: “Energy Equivalents” calculator.

This quotient is approximately (symbol = Hz), which is expressed
here at a precision of better than one part per billion—better
precision than the watt balance will be able to operate at for the
foreseeable future.

A “sum of photon frequencies” means the frequency (photon energy)
that is equivalent to one kilogram could theoretically be that of a
single photon oscillating at about , two photons that each have
half that frequency (about ), 100 photons with one hundredth the
specified value (about ), or approximately photons from a chemical oxygen-iodine laser,
which oscillate at about . This sum of frequencies is an
extraordinarily high value; a single photon oscillating at would be
oscillating over a trillion-trillion times faster than the
highest-energy gamma ray photons ever
observed.

Fortunately, the kilogram’s mass/energy equivalence is established
indirectly in the watt balance; gravity serves as a
crucial translation tool that is exploited to measure the “mass vs.
energy” relationship via a “force vs. electrical power”
relationship. Since gravity is the weakest of nature’s fundamental forces and since earth’s
gravity is relatively modest compared to other celestial bodies,
only a relatively small amount of electrical power is required to
counter the weight of one kilogram on earth. However, the force of
gravity varies significantly—nearly one percent—depending upon
where on earth’s surface the measurement is made (see Earth’s gravity ). Even more
problematic, there are subtle seasonal variations in gravity due to
changes in underground water tables, and even semimonthly and
diurnal changes due to tidal distortions in the earth’s shape
caused by the moon. Although gravity would not be a term in the
definition of the kilogram, gravity would be a crucial
term used in the delineation of the kilogram when relating
energy to power. Accordingly, the ‘gravity’ term must be measured
with at least as much precision and accuracy as are the other
terms. It is therefore highly desirable that gravity measurements
also be traceable to fundamental constants of nature. For the most
precise work in mass metrology, gravitational acceleration is
measured using dropping-mass absolute gravimeters that contain an iodine-stabilized
helium–neon laserinterferometer. The fringe-signal, frequency-sweep output from the interferometer is
measured with a rubidium atomic clock.
Since this type of dropping-mass gravimeter derives its accuracy
and stability from the constancy of the speed of light as well as
the innate properties of helium, neon, and rubidium atoms, the
‘gravity’ term in the delineation of an all-electronic kilogram is
also measured in terms of invariants of nature—and with very high
precision. For instance, in the basement of the NIST’s Gaithersburg
facility in 2009, when measuring the gravity acting upon Pt 10Ir
test masses (which are denser, smaller, and have a slightly lower
center of gravity inside the watt balance than stainless steel
masses), the measured value was typically within 8 ppb of
.

The virtue of electronic realizations like the watt balance is that
the definition and dissemination of the
kilogram would no longer be dependent upon the stability of
kilogram prototypes, which must be very carefully handled and
stored. It would free physicists from the need to rely on
assumptions about the stability of those prototypes, including
those that would be manufactured under atom-counting schemes.
Instead, hand-tuned, close-approximation mass standards would
simply be weighed and documented as being equal to one kilogram
plus an offset value. With the watt balance, the kilogram would not
only be be delineated in electrical and gravity terms, all
of which are traceable to invariants of nature; it would be
defined in electrical terms in a manner that is directly
traceable to just two fundamental constants of nature. Mass
artifacts—physical objects calibrated in a watt balance, including
the IPK—would become transfer
standards.

Scales like the watt balance also permit more flexibility in
choosing materials with especially desirable properties for mass
standards. For instance, Pt 10Ir could continue to be used so that
the specific gravity of newly produced mass standards would be the
same as existing national primary and check standards (≈21.55
g/ml). This would reduce the relative uncertainty when making
mass comparisons in air. Alternately, entirely different
materials and constructions could be explored with the objective of
producing mass standards with greater stability. For instance,
osmium-iridium alloys could be investigated
if platinum’s propensity to absorb hydrogen (due to catalysis of
VOCs and hydrocarbon-based cleaning solvents) and atmospheric
mercury proved to be sources of
instability. Also, vapor-deposited, protective ceramic coatings
like nitrides could be investigated
for their suitability to isolate these new alloys.

The challenge with watt balances is not only in reducing their
uncertainty, but also in making them truly practical
realizations of the kilogram. Nearly every aspect of watt balances
and their support equipment requires such extraordinarily precise
and accurate, state-of-the-art technology that—unlike a device like
an atomic clock—few countries would currently choose to fund their
operation. For instance, the NIST’s watt balance used
four resistance standards in 2007, each of which was rotated
through the watt balance every two to six weeks after being
calibrated in a different part of NIST
headquarters facility in Gaithersburg, Maryland. It was found that simply moving the
resistance standards down the hall to the watt balance after
calibration altered their values 10 ppb (equivalent to 10 µg) or more.
Present-day technology is insufficient to permit stable operation
of watt balances between even biannual calibrations. If the
kilogram is defined in terms of the Planck constant, it is likely
there will only be a few—at most—watt balances initially operating
in the world.

Ampere-based force

This approach would define the kilogram as “the mass which would be
accelerated at precisely when subjected to the per-meter force
between two straight parallel conductors of infinite length, of
negligible circular cross section, placed one meter apart in
vacuum, through which flow a constant current of
(≈6,241,509,647,120,417,390) elementary charges per second.”

Effectively, this would define the kilogram as a derivative of the
ampere rather than present relationship,
which defines the ampere as a derivative of the kilogram. This
redefinition of the kilogram would specify elementary charge (e) as precisely coulomb rather than the current 2006 CODATA value of
. Effectively, the coulomb would be the sum of
6,241,509,647,120,417,390 elementary charges. It would necessarily
follow that the ampere (one coulomb per second) would also become
an electrical current of this precise quantity of elementary
charges per second passing a given point in an electric
circuit.

The virtue of a practical realization based upon this definition is
that unlike the watt balance and other scale-based methods, all of
which require the careful characterization of gravity in the
laboratory, this method delineates the magnitude of the kilogram
directly in the very terms that define the nature of mass:
acceleration due to an applied force. Unfortunately, it is
extremely difficult to develop a practical realization based upon
accelerating masses. Experiments over a period of years in Japan
with a superconducting, 30 g mass
supported by diamagnetic levitation
never achieved an uncertainty better than ten parts per million.
Magnetic hysteresis
was one of the limiting issues. Other groups are continuing this
line of research using different techniques to levitate the
mass.

R. Steiner, A Watt Balance On Its Side, NIST, 24 September
2007.

SI multiples

Because SI prefixes may not be
concatenated (serially linked) within the name or symbol for a unit
of measure, SI prefixes are used with the gram, not the kilogram, which already has a prefix
as part of its name.BIPM: SI Brochure: Section 3.2, The kilogram For instance, one-millionth of a kilogram
is 1 mg (one milligram), not 1 µkg (one microkilogram).

When the Greek lowercase “µ” (mu) in the symbol of microgram is
typographically unavailable, it is occasionally—although not
properly—replaced by Latin lowercase “u”.

The microgram is often abbreviated “mcg”, particularly in
pharmaceutical and nutritional supplement labeling, to avoid
confusion since the “µ” prefix is not well recognized outside of
technical disciplines.The practice of using the abbreviation “mcg”
rather than the SI symbol “µg” was formally mandated for medical
practitioners in 2004 by the Joint Commission on Accreditation of
Healthcare Organizations (JCAHO) in their “Do Not Use” List: Abbreviations, Acronyms, and
Symbols because hand-written expressions of “µg” can be
confused with “mg”, resulting in a thousand-fold overdosing. The
mandate was also adopted by the Institute for Safe Medication Practices. Note
however, that the abbreviation “mcg”, is also the
symbol for an obsolete CGS unit of measure
known as the “millicentigram”, which is equal to 10 µg.

The unit name “megagram” is rarely used, and even then,
typically only in technical fields in contexts where especially
rigorous consistency with the units of measure is desired. For most
purposes, the unit “tonne” is instead used.
The tonne and its symbol, t, were adopted by the CIPM in 1879. It
is a non-SI unit accepted by the BIPM for use with the SI. In
English speaking countries it is usually called “metric ton”.BIPM:
SI Brochure: Section 4.1, Non-SI units accepted for use with
the SI, and units based on fundamental Note also that the unit name
“megatonne” or “megaton” (Mt) is often used in general-interest
literature on greenhouse gas
emissions whereas the equivalent value in scientific papers on the
subject is often the “teragram” (Tg).

Glossary

Abstracted: Isolated and its effect changed in
form, often simplified or made more accessible in the process.

Artifact: A simple human-made object used
directly as a comparative standard in the measurement of a physical
quantity.

Check standard:

# A standard body’s backup replica of the International
Prototype Kilogram (IPK).

# A secondary kilogram mass standard used as a stand-in for the
primary standard during routine calibrations.

Definition: A formal, specific, and exact
specification.

Delineation: The physical means used to mark a
boundary or express the magnitude of an entity.

Disseminate: To widely distribute the
magnitude of a unit of measure, typically via replicas and transfer
standards.

IPK: Abbreviation of “International Prototype
Kilogram” (CG image),
the mass artifact in France internationally recognized as
having the defining mass of precisely one kilogram.

Magnitude: The extent or numeric value of a
property

National prototype: A replica of the IPK
possessed by a nation.

Practical realization: A readily reproducible
apparatus to conveniently delineate the magnitude of a unit of
measure.

Primary national standard:

# A replica of the IPK possessed by a nation

# The least used replica of the IPK when a nation possesses
more than one.

Prototype:

# A human-made object that serves as the defining comparative
standard in the measurement of a physical quantity.

# A human-made object that serves as the comparative
standard in the measurement of a physical quantity.

# The IPK and any of its replicas

Replica: An official copy of the IPK.

Sister copy: One of six official copies of the
IPK that are stored in the same safe as the IPK and are used as
check standards by the BIPM.

Transfer standard: An artifact or apparatus
that reproduces the magnitude of a unit of measure in a different,
usually more practical, form.

Notes

References

The spelling kilogram is the modern spelling used by
the International Bureau of Weights and Measures (BIPM), the U.S.
National Institute of Standards and Technology (NIST), the U.K.’s
National Measurement Office, National Research Council Canada, and
Australia’s National Measurement Institute. The traditional
British-English spelling kilogramme is sometimes also
used.

The same decree also defined the liter as follows: “Liter: the
measure of volume, both for liquid and solids, for which the
displacement would be that of a cube [with sides measuring]
one-tenth of a meter.” Original text: “Litre, la mesure de
capacité, tant pour les liquides que pour les matières sèches, dont
la contenance sera celle du cube de la dixièrne partie du
mètre.”

Modern measurements show the temperature at which water reaches
maximum density is 3.984 °C. However, the scientists at the close
of the 18th century concluded that the temperature was 4 °C.

The other two Pt 10Ir standards owned by the U.S. are K79, from
a new series of prototypes that were diamond-turned directly to a
finish mass, and K85, which is used for watt balance experiments
(see Watt
balance, above).

The combined relative standard uncertainty (CRSU) of these
measurements, as with all other tolerances and uncertainties in
this article unless otherwise noted, have a 1σ standard deviation,
which equates to a confidence level of about 68%; that is to say,
68% of the measurements fall within the stated tolerance.

The Planck constant’s unit of measure “joule-second” (J·s) may
be more easily understood when expressed as a “joule per hertz” (J/Hz). Universally, an individual photon has
an energy that is proportional to its frequency. This relationship
is and .

R. Steiner, Watts in the watt balance, NIST,
16 Oct. 2009.

R. Steiner, No FG-5?, NIST, 30 Nov. 2007. “We rotate
between about 4 resistance standards, transferring from the
calibration lab to my lab every 2–6 weeks. Resistors do not
transfer well, and sometimes shift at each transfer by 10 ppb or
more.”